Advertisement

Acta Mechanica Solida Sinica

, Volume 22, Issue 5, pp 465–473 | Cite as

Analysis of a Crack in a Functionally Graded Strip with a Power Form Shear Modulus

  • Jinju Ma
  • Zheng Zhong
  • Chuanzeng Zhang
Article

Abstract

The plane strain problem of a crack in a functionally graded strip with a power form shear modulus is studied. The governing equation in terms of Airy’s stress function is solved exactly by means of Fourier transform. The mixed boundary problem is then reduced to a system of singular integral equations and is solved numerically to obtain the stress intensity factor at crack-tip. The maximum circumferential stress criterion and the strain energy density criterion are both employed to predict the direction of crack initiation. Numerical examples are given to show the influence of the material gradation models and the crack sizes on the mode-I and mode-II stress intensity factors. The dependence of the critical kink-angle on the crack size is examined and it is found that the crack kink-angle decreases with the increase of the normalized crack length, indicating that a longer crack tends to follow the original crack-line while it is much easier for a shorter crack to deviate from the original crack-line.

Key words

functionally graded material crack stress intensity factors fracture criterion 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Delale, F. and Erdogan, F., The crack problem for a nonhomogeneous plane. Journal of Applied Mechanics, 1983, 50(3): 609–614.CrossRefGoogle Scholar
  2. [2]
    Chen, Y.F. and Erdogan, F., The interface crack problem for a non-homogeneous coating bonded to a homogeneous substrate. Journal of the Mechanics and Physics of Solids, 1996, 44(5): 771–787.CrossRefGoogle Scholar
  3. [3]
    Shbeeb, N.I. and Binienda, W.K., Analysis of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness. Engineering Fracture Mechanics, 1999, 64(6): 693–720.CrossRefGoogle Scholar
  4. [4]
    Zhong, Z., Shu, D.W. and Jin, B., Analysis of a mode III crack in a functionally gradient piezoelectric material. Materials Science Forum, 2003, 423–425: 623–628.CrossRefGoogle Scholar
  5. [5]
    Hu, K.Q., Zhong, Z. and Jin, B., Anti-plane shear crack in a functionally gradient piezoelectric layer bonded to dissimilar half spaces. International Journal of Mechanical Sciences, 2005, 47: 82–93.CrossRefGoogle Scholar
  6. [6]
    Hu, K.Q. and Zhong, Z., A moving mode-III crack in a functionally graded piezoelectric strip. International Journal of Mechanics and Materials in Design, 2005, 2: 61–79.CrossRefGoogle Scholar
  7. [7]
    Guo, L.C. and Noda, N., Modeling method for a crack problem of functionally graded materials with arbitrary properties — piecewise-exponential model. International Journal of Solids and Structures, 2007, 44(21): 6768–6790.CrossRefGoogle Scholar
  8. [8]
    Cheng, Z.Q. and Zhong, Z., Analysis of a moving crack in a functionally graded strip between two homogeneous layers. International Journal of Mechanical Sciences, 2007, 49(9): 1038–1046.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Zhang, Ch., Sladek, J. and Sladek, V., Crack analysis in unidirectionally and bidirectionally functionally graded materials. International Journal of Fracture, 2004, 129: 385–406.CrossRefGoogle Scholar
  10. [10]
    Zhang, Ch., Sladek, J. and Sladek, V., Antiplane crack analysis of a functionally graded material by a BIEM. Computational Materials Science, 2005, 32: 611–619.CrossRefGoogle Scholar
  11. [11]
    Huang, G.Y., Wang, Y.S. and Yu, S.W., Fracture analysis of a functionally graded interfacial zone under plane deformation. International Journal of Solids and Structures, 2004, 41(3–4): 731–743.CrossRefGoogle Scholar
  12. [12]
    Huang, G.Y., Wang, Y.S. and Yu, S.W., A new model for fracture analysis of functionally graded coatings under plane deformation. Mechanics of Materials, 2005, 37(4): 507–516.CrossRefGoogle Scholar
  13. [13]
    Cheng, Z.Q. and Zhong, Z., Fracture analysis of a functionally graded strip under plane deformation. Acta Mechanica Solida Sinaca, 2006, 19(2): 114–121.CrossRefGoogle Scholar
  14. [14]
    Cheng, Z.Q. and Zhong, Z., Fracture analysis of a functionally graded interfacial zone between two dissimilar homogeneous materials. Science in China G: Physics, Mechanics & Astronomy, 2006, 49(5): 540–552.CrossRefGoogle Scholar
  15. [15]
    Zhong, Z. and Cheng, Z.Q., Fracture analysis of a functionally graded strip with arbitrary distributed material properties. International Journal of Solids and Structures, 2008, 45(13): 3711–3725.CrossRefGoogle Scholar
  16. [16]
    Gu, P. and Asrao, R.J., Crack deflection in functionally graded materials. International Journal of Solids and Structures, 1997, 34(24): 3085–3098.CrossRefGoogle Scholar
  17. [17]
    Jain, N., Rousseau, C.E. and Shukla, A., Crack-tip stress fields in functionally graded materials with linearly varying properties. Theoretical and Applied Fracture Mechanics, 2004, 42(2): 155–170.CrossRefGoogle Scholar
  18. [18]
    Wang, X.Y., Zou, Z.Z. and Wang, D., On the Griffith crack in a nonhomogeneous interlayer of adjoining two different elastic materials. International Journal of Fracture, 1996, 79(3): R51–R56.CrossRefGoogle Scholar
  19. [19]
    Li, C., Weng, G.J., Duan, Z. and Zou, Z., Dynamic stress intensity factor of a functionally graded material under antiplane shear loading. Acta Mechanica, 2001, 149(1): 1–10.CrossRefGoogle Scholar
  20. [20]
    Xu, H.M., Yao, X.F., Feng, X.Q. and Yeh, H.Y., Fundamental solution of a power-law orthotropic and halfspace functionally graded material under line loads. Composites Science and Technology, 2008, 68(1): 27–34.CrossRefGoogle Scholar
  21. [21]
    Erdogan, F. and Gupta, G.D., On the numerical solution of singular integral equations. Quarterly of Applied Mathematics, 1972, 29(4): 525–534.MathSciNetCrossRefGoogle Scholar
  22. [22]
    Erdogan, F. and Sih, G.C., On the rack extension in plates under plane loading and transverse shear. ASME Journal of Basic Engineering, 1963, 4: 519–525.CrossRefGoogle Scholar
  23. [23]
    Sih, G.C. and Macdonald, D., Fracture mechanics applied to engineering problems-strain energy density fracture criterion. Engineering Fracture mechanics, 1974, 6: 361–386.CrossRefGoogle Scholar
  24. [24]
    Kim, J.H. and Paulino, G.H., On fracture criteria for mixed-mode crack propagation in functionally graded materials. Mechanics of Advanced Materials and Structures, 2007, 14(4): 227–244.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2009

Authors and Affiliations

  1. 1.School of Aerospace Engineering and Applied MechanicsTongji UniversityShanghaiChina
  2. 2.Department of Civil EngineeringUniversity of SiegenSiegenGermany

Personalised recommendations